David Cameron has signalled that George Osborne may revise his plans to impose a cap on tax relief for philanthropic gifts, amid warnings that the government is placing at risk vital donations to charities.

At the launch of a £600m fund to support grassroots social projects as part of his “big society” initiative, the prime minister pledged to listen to charities to ensure the budget did not have a harmful impact on donations.

Cameron acknowledged the concerns of charities after protests at the chancellor’s decision to crack down on people who make unlimited use of tax reliefs “year after year”.

Osborne said in the budget: “From next year anyone seeking to claim more than £50,000 of these reliefs in any one year will have a cap set at 25% of their income. We’ve capped benefits. Now it’s right to cap tax reliefs too.”

It is understood that Jeremy Hunt, the culture secretary, has led complaints within government that the Osborne plan will discourage philanthropic donations. The chancellor’s announcement, which was part of his plans to crack down on aggressive tax avoidance, appeared to contradict an announcement by Hunt last year about trying to create a US-style tradition of philanthropy in Britain.

Cameron said: “I know there are some concerns that the budget signals a weakening of our commitment to philanthropy. Let me make it clear. I want to see more, not less, philanthropic giving. That is at the heart of my vision of a bigger society where we rely more on each other and less on the state. That is why we are reducing inheritance tax for those estates that leave 10% or more to charity.

“We are bringing in a generous relief for those donating collections to the nation. We are working to streamline and simplify gift aid. But just as they do in the US, a country renowned for its philanthropy, we are capping tax reliefs because of the principle that everyone should pay some income tax. Even with the new cap individuals can still claim up to £50,000 in reliefs or a quarter of their income, whichever is the greater.

“However, as the chancellor said at the time of the budget, we want to engage with you and with everyone in the philanthropic sector to make sure this doesn’t have a harmful impact on philanthropic giving, particularly on those charities that can be dependent on large donations.”

The prime minister attempted to breathe fresh life into his flagging big society idea with the launch of the £600m fund. He announced that £400m from dormant bank accounts would be used to help finance the scheme, dubbed Big Society Capital. A further £200m will come from Britain’s four largest high street banks – Barclays, Lloyds, HSBC and RBS.

The fund will help local groups take control of their post office and provide capital for charities and voluntary groups bidding for government contracts. There will be a strong focus on helping the long-term unemployed back into work.

Cameron, who has faced criticism for failing to define the big society, hailed the scheme as one of the world’s most important social investment funds. He hopes it will show that the big society is more than just an election slogan.

Cameron declared on the eve of the Tory manifesto launch before the general election that he was inviting the British people to join his government as part of an open, big society. But many Tories said the idea, seen as the brainchild of Cameron’s policy guru Steve Hilton, was ill-defined and difficult to explain.

Ministers say it has taken two years to establish the fund, which will be run independently of the government by the former JP Morgan global head of research Nick O’Donohoe, and chaired by Sir Ronald Cohen, the Apax founder.

The European commission had to declare that the fund did not break its state aid rules. There were lengthy negotiations with the high street banks who made £200m of capital available under the terms of the Merlin deal with the government.

The prime minister said: “For years, the City has been associated with providing capital to help businesses to expand. Today, this is about supplying capital to help society expand. Just as finance from the City has been essential to help businesses grow and take on the world, so finance from the City is going to be essential to helping tackle our deepest social problems.”

A Tory source said: “The budget was explicit that we will proactively explore with philanthropists ways to ensure this new limit will not significantly impact upon charities that depend on large donations. The prime minister simply restated that position today. I don’t think it can be described as a ‘rethink’.”